Linear momentum Transitional Reasoning Download PDF

Questions

1. 1.

   A ballistic test block with a mass of 1.8 kg rests on a smooth, frictionless horizontal surface. A high-speed pellet with a mass of 0.050 kg is fired horizontally into the block at an initial speed of 240 m/s. The pellet passes straight through the block and emerges along the same horizontal line with a reduced speed of 80 m/s. What is the magnitude of the linear momentum of the block immediately after the pellet emerges?

   • A) 8.0 kg·m/s
   • B) 12 kg·m/s
   • C) 16 kg·m/s
   • D) 4.0 kg·m/s
2. 2.

   On a straight horizontal freight yard track with negligible friction, a 600 kg service locomotive coasts at a constant speed of 10 m/s toward a stationary 400 kg cargo wagon. The locomotive collides with the wagon and an automatic coupler locks them together, causing them to move forward as a single combined unit. What is the magnitude of the linear momentum of the cargo wagon immediately after the coupling?

   • A) 3000 kg m/s
   • B) 3600 kg m/s
   • C) 4000 kg m/s
   • D) 2400 kg m/s
3. 3.

   In an orbital servicing simulation, two docking modules drift along a shared straight alignment rail. Module A has a mass of 450 kg and moves in the positive reference direction at a constant speed of 2.0 m/s. Module B has a mass of 300 kg and moves in the opposite, negative reference direction at a constant speed of 1.5 m/s. What is the total linear momentum of the two-module system?

   • A) 1350 kg·m/s in the positive direction
   • B) 450 kg·m/s in the positive direction
   • C) 375 kg·m/s in the positive direction
   • D) 450 kg·m/s in the negative direction
4. 4.

   During an outdoor ballistics test, a projectile with a mass of 0.40 kg is launched from ground level with an initial speed of 25 m/s at an angle of 53° above the horizontal. Assuming aerodynamic drag is negligible throughout the flight, what is the magnitude of the projectile's linear momentum at the highest point of its trajectory? (Use $\cos 53^\circ = 0.60$ and $\sin 53^\circ = 0.80$.)

   • A) 0 kg·m/s
   • B) 10 kg·m/s
   • C) 6.0 kg·m/s
   • D) 8.0 kg·m/s
5. 5.

   A deep-space exploration capsule with a total mass of 8.0 kg coasts in a straight line at a constant speed of 15 m/s in the absence of net external forces. An internal spring mechanism activates, separating the capsule into two distinct components, X and Y, along the original line of motion. Component X has a mass of 5.0 kg and continues in the forward direction at 21 m/s immediately following the separation. What is the linear momentum of component Y immediately after separation?

   • A) 45 kg·m/s in the forward direction
   • B) 45 kg·m/s in the backward direction
   • C) 15 kg·m/s in the forward direction
   • D) 15 kg·m/s in the backward direction
6. 6.

   A sensor-equipped test ball with a mass of 0.25 kg travels horizontally at a constant speed of 16 m/s toward a vertical rebound wall. After striking the wall perpendicularly, the ball rebounds horizontally along its original line of approach with a speed of 12 m/s. What is the magnitude of the change in the ball's linear momentum as a result of the collision?

   • A) $1.0\text{ kg}\cdot\text{m/s}$
   • B) $3.0\text{ kg}\cdot\text{m/s}$
   • C) $7.0\text{ kg}\cdot\text{m/s}$
   • D) $4.0\text{ kg}\cdot\text{m/s}$
7. 7.

   A commuter train travels along a straight horizontal track due west at a constant speed of 20 m/s relative to the ground. Inside one of the passenger cars, an inspection officer with a mass of 70 kg walks down the central aisle due east at a steady speed of 2.0 m/s relative to the train. What is the linear momentum of the inspection officer relative to an observer standing stationary on the ground?

   • A) 1540 kg·m/s due west
   • B) 1260 kg·m/s due west
   • C) 1260 kg·m/s due east
   • D) 140 kg·m/s due east
8. 8.

   A remote-controlled cargo carrier with a mass of 10 kg starts from rest on a straight horizontal track. Its propulsion motor delivers a constant net forward force of 25 N for 4.0 s, after which a regenerative braking system exerts a constant opposing force of 15 N for 3.0 s. Assuming all motion occurs along the same straight line, what is the magnitude of the final linear momentum of the carrier at the end of this 7.0 s interval?

   • A) 45 kg·m/s
   • B) 55 kg·m/s
   • C) 100 kg·m/s
   • D) 145 kg·m/s
9. 9.

   In an automated distribution center, two automated guided vehicles move across a flat concrete floor. Vehicle P has a total mass of 20 kg and travels due north at a constant speed of 4.0 m/s, while Vehicle Q has a total mass of 15 kg and travels due east at a constant speed of 4.0 m/s. What is the magnitude of the total linear momentum of the two-vehicle system?

   • A) 140 kg·m/s
   • B) 100 kg·m/s
   • C) 70 kg·m/s
   • D) 20 kg·m/s
10. 10.

    A student analyzes the telemetry data of two test carts, Cart X of mass 2 kg and Cart Y of mass 6 kg, traveling in the positive direction along a straight horizontal track. The sensors record that Cart X has a kinetic energy of 36 J, while Cart Y has a kinetic energy of 12 J. Which of the following correctly compares the magnitudes of the linear momenta of the two carts?

    • A) Their linear momentum magnitudes are equal because linear momentum magnitude is given by $p = \sqrt{2mK}$, yielding 12 kg·m/s for each cart.
    • B) Cart X has three times the linear momentum magnitude of Cart Y because linear momentum is directly proportional to kinetic energy.
    • C) Cart Y has three times the linear momentum magnitude of Cart X because an object with three times the mass always carries three times the momentum.
    • D) Cart X has a greater linear momentum magnitude because its velocity is three times greater than that of Cart Y.